Congrats on a nice unmolested/converted BSR. You have a 3.A. version of the BSR contract revolvers.
Ed is right, shipped 1/16, more precisely in a group shipped Jan. 6, 1916. We don't have a source for manufacturing dates, but these were shipped is many smaller group shipments ASAP for the war so it's highly likely it was completed within weeks or even days before shipping.
More details on this version below:
3.A. ".455 Mark II HE - 2nd Model" (sans extractor barrel shroud and 3rd lock), but with cylinder pin hole reduced .020" and the Ext Rod is reduced .020" in diameter (Neal & Jinks Pg. 215-16) from versions 1. the ".44 HE 1st Model Triple Lock" factory converted to .455, and 2. the ".455 HE 1st Model Triple Lock" produced in .455. This version was referred to as the MK II revolver by the British and stamped 'II' by them, left side frame.
The 2nd Model continued in the .455 1st Model TL Brit serial range beginning ~#5801 (previously thought to be 5462) to #74755, shipped 1915-17.
By Feb 1916 724 were manufactured for the Canadians, chambered in 45 Colt, without a cartridge roll mark on barrel, presumed for the RCMP [H of S&W, pg. 203].
Another 15 in 45 Colt were sold commercially in 1916; likely "over run" guns from the above order.
The Canadian military also bought 14,500* .455 2nd Models [H of S&W, pg. 203].
And 1105 2nd Models were released for commercial sales in the US, shipped Dec 1917 to Shapleigh Hardware in St. Louis [S&W, N&J pg. 216].
*Canadian military shipments of 14,500:
-1500 Shipped after Aug. 1915
-850 Shipped thru December 24th, 1915
-150 Shipped thru March 31st, 1916
-6000 Shipped thru July 22nd, 1916
-6000 Shipped February 10, 1917
At least 1 #728XX shipped July 29th, 1916, see post #10:
http://smith-wessonforum.com/s-w-ha...5-455-hand-ejector-45-colt.html#post139027072
Since your gun does not sound like it has any proof/export stamps, it came back home to the USA thru "unofficial channels". In other words in a soldier's duffel bag, with a Navy sailor or merchant marine aboard a com'l ship, mailed home, in a tourist's suitcase after the war, across the border in the trunk of a car, etc.
If it had the full nine yards of proof/export stamps, it would have been exported by an English/Canadian company to a USA import company. And w/o those stamps we have no way of knowing how long ago that might have happened.